Dimension Reduction for Regression with Bottleneck Neural Networks

Dimension reduction for regression (DRR) deals with the problem of finding for high-dimensional data such low-dimensional representations, which preserve the ability to predict a target variable. We propose doing DRR using a neural network with a low-dimensional "bottleneck" layer. While the network is trained for regression, the bottleneck learns a low-dimensional representation for the data. We compare our method to Covariance Operator Inverse Regression (COIR), which has been reported to perform well compared to many other DRR methods. The bottleneck network compares favorably with COIR: it is applicable to larger data sets, it is less sensitive to tuning parameters and it gives better results on several real data sets.